Merge branch 'bool-leb2' into 'master'

alternative overlay for coq/coq#12162

See merge request iris/stdpp!159

tests/numbers.ref

+le
+     : nat → nat → Prop
+lt
+     : nat → nat → Prop
+le
+     : nat → nat → Prop
+lt
+     : nat → nat → Prop
+le
+     : nat → nat → Prop
+lt
+     : nat → nat → Prop
+le
+     : nat → nat → Prop
+lt
+     : nat → nat → Prop

tests/numbers.v

+From stdpp Require base numbers prelude.
+
+(** Check that we always get the [le] and [lt] functions on [nat]. *)
+Module test1.
+  Import stdpp.base.
+  Check le.
+  Check lt.
+End test1.
+
+Module test2.
+  Import stdpp.prelude.
+  Check le.
+  Check lt.
+End test2.
+
+Module test3.
+  Import stdpp.numbers.
+  Check le.
+  Check lt.
+End test3.
+
+Module test4.
+  Import stdpp.list.
+  Check le.
+  Check lt.
+End test4.

theories/base.v

@@ -3,7 +3,10 @@ that are used throughout the whole development. Most importantly it contains
 abstract interfaces for ordered structures, sets, and various other data
 structures. *)
 
-From Coq Require Export Morphisms RelationClasses List Bool Utf8 Setoid.
+(* We want to ensure that [le] and [lt] refer to operations on [nat].
+These two functions being defined both in [Coq.Bool] and in [Coq.Peano],
+we must export [Coq.Peano] later than any export of [Coq.Bool]. *)
+From Coq Require Export Morphisms RelationClasses List Bool Utf8 Setoid Peano.
 From Coq Require Import Permutation.
 Set Default Proof Using "Type".
 Export ListNotations.